Answer:
The inductance of the inductor is 19.3 mH
Explanation:
Inductance can be calculated from capacitive reactance,and it is given as;
[tex]X_l = \omega L\\\\L = \frac{X_l}{\omega}\\\\L = \frac{X_l}{2\pi f}[/tex]
Apply ohms law to replace the capacitive reactance by voltage and current;
[tex]L = \frac{X_l}{2\pi f}\\\\L = X_L(\frac{1}{2\pi f} )\\\\L = \frac{V}{I} (\frac{1}{2\pi f})[/tex]
Substitute the given values;
[tex]L = \frac{V}{I} (\frac{1}{2\pi f})\\\\L = \frac{43}{46*10^{-3}} (\frac{1}{2\pi (7.7*10^3)})\\\\L = 0.0193 \ H\\\\L = 19.3 \ mH[/tex]
Therefore, the inductance of the inductor is 19.3 mH
